Satellite changing distance as θ changes how?

  • Thread starter Thread starter LearninDaMath
  • Start date Start date
  • Tags Tags
    Satellite
AI Thread Summary
The discussion centers on how the distance (h) of an Earth-observing satellite from the Earth's surface changes as the angle (θ) detected by its horizon sensors varies. As θ increases, h decreases, indicating that the satellite is getting closer to the Earth. This relationship suggests that the satellite's position alters relative to the Earth's curvature, but does not imply any movement of the Earth itself. The participants also explore the graphical representation of trigonometric functions related to this scenario, particularly focusing on how to visualize the changes in h and θ. Overall, the interaction emphasizes understanding the geometric and trigonometric principles at play in satellite observation.
LearninDaMath
Messages
295
Reaction score
0
note

Please note: I am not asking for the answer, nor am I asking how to solve a) or b). This question is about what it means that h is changing as θ is changing.

textbook question

An Earth observing satellite can see only a portion of the Earth's surface. The satellite has horizon sensors that can detect the angle θ shown in the accompanying figure. Let r be the radius of the Earth and h the distance of the satellite from the Earth's surface.

a) show that h = r(cscθ -1)

b)Using r = 6378km, find the rate at which h is changing with respect to θ when θ = 30 degrees. Express in km/degree

question

The illustration for this question is:
satellite.png


How/why is h changing as the angle changes? Does this imply the Earth is traveling in some direction or rotating? Or does it imply the satellite is changing is traveling in some direction...or rotating? It seems like the answer is implying that the satelite getting closer to the Earth as the angle changes? Why?
 
Physics news on Phys.org
nevermind, i reasoned it out...is it correct, i don't know, but it makes sense to me :)
 
θ is the angle on the right hand side of the triangle, at the vertex where the satellite is.
When h is smaller (satellite closer to the Earth), the angle θ must be larger. As h changes, θ must change as well. Draw the diagram with h larger or smaller and you will see that θ has changed with h.
 
Thanks, that's what I concluded. Appreciate your response.

Would you be able to lend some insight on this question:

https://www.physicsforums.com/showthread.php?t=582325

It's a classic ladder question from my calc book. But its still physics. I have the correct answer and understand the process of getting to the correct answer.

However, there seems to be no graphical representation of what is going on. I am interested to know how a question like this would be represented graphically.

Since I'm using trig functions, f(θ) = sin(θ) specifically, would I represent the function as a sin graph? And then the derivative would be the line tangent to the sin function at θ = 60?

The derivative of sinθ is cosθ, so the slope of the tan would be cos(60) = 1/2.

However, the actual derivative is 1/2 * 10 since the original function is sin60 = x/10 , so I actually have 10cos60 = 10*1/2 = 5 = Mtan

So the slope of the tangent of sin(θ) at θ = 60 is 1/2 , however, the function in the question is 10sinθ = f(θ) = x ...so is the graph f(θ) = sin(θ) = x or f(θ) = 10sin(θ) = x ...or neither?
 
The function is x = 10*sin(θ). You could graph x vs θ and find the slope at θ = 60 to visualize your solution dx/dθ = 10*cos θ = 5.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Back
Top